中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
Emergent dynamics of Cucker-Smale flocking particles in a random environment

文献类型:期刊论文

AuthorHa, Seung-Yeal1,2,3; Jeong, Jiin4; Noh, Se Eun5; Xiao, Qinghua6; Zhang, Xiongtao4
SourceJOURNAL OF DIFFERENTIAL EQUATIONS
Issued Date2017-02-05
Volume262Issue:3Pages:2554-2591
KeywordCucker-Smale-Fokker-Planck equation Degenerate diffusion Flocking Mean-field limit
English AbstractWe present a new kinetic Cucker-Smale-Fokker-Planck (CS-FP) type equation with a degenerate diffusion, which describes the dynamics for an ensemble of infinitely many Cucker-Smale particles in a random environment. The asymptotic dynamics of the CS-FP equation exhibits a threshold-like phenomenon depending on the relative strength between the coupling strength and the noise strength. In the small coupling regime, the noise effect becomes dominant, which induces the velocity variance to increase to infinity exponentially fast. In contrast, the velocity alignment effect is strong in the large coupling regime, and the velocity variance tends to zero exponentially fast. We present the global existence of classical solutions to the CS-FP equation for a sufficiently smooth initial datum without smallness in its size. For the kinetic CS-FP equation with a metric dependent communication weight, we provide a uniform-in-time mean-field limit from the stochastic CS-model to the kinetic CS-FP equation without convergence rate. (C) 2016 Elsevier Inc. All rights reserved.
WOS HeadingsScience & Technology ; Physical Sciences
WOS SubjectMathematics
WOS Subject ExtendedMathematics
WOS Keyword PlusMEAN-FIELD LIMIT ; FOKKER-PLANCK EQUATION ; GLOBAL EXISTENCE ; ASYMPTOTIC FLOCKING ; COLLECTIVE MOTION ; MODEL ; SYSTEM ; DIMENSIONS ; SYNCHRONIZATION ; FORCES
Indexed TypeSCI
Language英语
WOS IDWOS:000392463200017